Yet another question from 2001 September exam (Q12b)

I dont understand why the solution is pulling out the chain rule here, then they say del-PV/del-i, to me this represents
the rate of change of present value with respect to i with other variables helf constant, whereas the question says define it to be "proportionate change in present value per unit change in i" which would be v(i)=(-dA/dI).(1/A) as i have done below in my attempt of this question. Is what i have done correct? I can understand my reasoning but i can not understand what the solution is trying to do.

 

This looks perfectly correct to me.

The reason they've used the chain rule in the Examiners Report (as far as I can see) is to tie the answer to (b) to the answer to (a). But if you don't like that approach, don't use it.